I am thinking of an integer in the interval [1-15]. You are to try to guess it by telling me intervals and I will tell you if my number lies in that interval.

For example if my number is 6 and you guess [6-9] I will tell yes but if you guess [7-11] I will tell you no but not if my number is higher or lower.

You win by guessing an interval of just one number and that number is my number. Find a strategy that minimizes the expected number of guesses.